序数

The name comes from the Latin ordinalis, "concerning order", and the distinction it marks is older than the word: a cardinal says how many, an ordinal says which one in a row. English has written ordinals as a numeral with a tail — 1st, 2nd, 3rd — since early modern printers began abbreviating, and the tail is simply the end of the spoken word. That is why the exception at 11, 12 and 13 needs no rule of its own: eleventh, twelfth and thirteenth all end in -th, so 11th, 12th and 13th do too, and 111th follows the teens rather than 1st.

Older abbreviations have not all died out. Eighteenth- and nineteenth-century English wrote 2d and 3d, clipping second and third harder, and American legal citation still does: the Federal Reporter's second and third series are cited F.2d and F.3d, and the appellate circuits as 2d Cir. and 3d Cir.

Romance languages abbreviated the ending rather than the word. Spanish primero and primera shrink to 1.º and 1.ª, the ending raised above the line; Italian writes 1º and 1ª without the stop. Those raised letters were given code points of their own in ISO/IEC 8859-1 in 1987 and are now U+00AA and U+00BA in Unicode — separate characters from the degree sign U+00B0 they are endlessly confused with. French abbreviates differently again: 1er, 1re, and then a bare e for everything after, which makes the very common 2ème a mistake in careful typography. German and Turkish need no letters at all, a full stop after the numeral doing the work, so 1. reads erste and birinci.

Georg Cantor carried the idea past the finite in 1883, defining transfinite ordinals to number positions in infinite well-ordered sets. And zeroth, now ordinary in computing, came in through physics: the name of the zeroth law of thermodynamics is generally credited to Ralph Fowler, who proposed it once the other three laws were already numbered.

主な性質

• In English the last two digits decide the suffix: 11, 12 and 13 take -th, so 111th, 112th and 113th follow the teens, not the units.
• Otherwise the last digit decides — 1 takes -st, 2 takes -nd, 3 takes -rd, and every other digit takes -th.
• The suffixes are the final letters of the spoken words, which is why the teens need no separate rule: eleventh, twelfth and thirteenth already end in -th.
• U+00BA MASCULINE ORDINAL INDICATOR (º) and U+00AA FEMININE ORDINAL INDICATOR (ª) are distinct characters from U+00B0 DEGREE SIGN (°); all three appear in ISO/IEC 8859-1.
• French abbreviates premier as 1er, première as 1re and all later ordinals with a single e — 2e, 3e, 21e — so the widespread 2ème is not the recommended form.
• German and Turkish mark an ordinal with a full stop after the numeral: 1. is erste in German and birinci in Turkish.
• Turkish ordinals are a suffix harmonised to the stem vowel — birinci, ikinci, üçüncü, dördüncü, altıncı — and can be written on a numeral after an apostrophe.
• Dutch writes 1e, 2e and 3e, with the longer 1ste, 2de and 3de equally standard.

登場する場面

• Dates in English speech and writing take an ordinal on the day — the 4th of July, the 1st of May — even where the written date shows a bare numeral.
• American legal citation: the Federal Reporter second and third series are cited F.2d and F.3d, and the federal appellate circuits as 2d Cir. and 3d Cir.
• Regnal and papal names are Roman numerals read as ordinals: Elizabeth II is spoken "Elizabeth the Second".
• Zero-based indexing makes "the zeroth element" ordinary usage among programmers — a borrowing from the zeroth law of thermodynamics rather than from older mathematics.
• Word processors autocorrect 1st into a raised 1ˢᵗ; several style guides advise against the superscript in running text, so it is a house preference rather than a rule.